"Among the changes in U.S. poverty policy coming about from the end of "welfare as we knew it" has been an imposition of time limits on the receipt of federal welfare funds. Yet little is known about the impact this restriction will have. This paper examines welfare dynamics under Aid to Families with Dependent Children to provide a sense of magnitude of the number of families that would have been at risk of exhausting their eligibility for federal funds in the past. In addition, simulation models are employed to assess whether these results are sensitive to changes in key variables, some of which are within the grasp of policy makers, others of which are not. (JEL" 13, J1) Copyright 1999 Western Economic Association International.